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An improved macro–micro-two-scale model to predict high-cycle fatigue life under variable amplitude loading

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Abstract

This study is based on continuum damage mechanics and constructs an improved macro–micro-two-scale model to predict the fatigue life of engineering metallic materials subjected to variable amplitude loading. To account quantitatively for the fatigue damage retarding effect of higher load on lower ones in a loading sequence, the cyclic plastic response curve of microscopic weak inclusion is independently designed. Meanwhile, an improved two-scale fatigue damage model in rate form is proposed by introducing a new exponent function acted on the equivalent plastic strain term in the model for taking account of fatigue mean stress effect under variable amplitude loading. The parameters of the two-scale fatigue damage model are identified through an inverse approach based on fatigue test results under constant amplitude loading. The predictive accuracy of the proposed model is validated by fatigue test data of Al 2024-T3 standard coupon and plate with a hole under different variable amplitude loading.

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References

  1. Huang, W., Sridhar, N.: Fatigue failure risk assessment for a maintained Stiffener-Frame welded structure with multiple site cracks. Int. J. Appl. Mech. 8(1), 1650024 (2016)

    Article  Google Scholar 

  2. Hull, D., Bacon, D.J.: Introduction to dislocations. Butterworth-Heinemann, Oxford (2011)

    Google Scholar 

  3. Gupta, A., Sun, W., Bennett, C.J.: Simulation of fatigue small crack growth in additive manufactured Ti-6Al-4V material. Continuum Mech. Thermodyn. (2020). https://doi.org/10.1007/s00161-020-00878-0

  4. Bandara, C.S., Siriwardane, S.C., Dissanayake, U.I., et al.: Developing a full range S-N curve and estimating cumulative fatigue damage of steel elements. Comput. Mater. Sci. 96, 96–101 (2015)

    Article  Google Scholar 

  5. Todinov, M.T.: Necessary and sufficient condition for additivity in the sense of Palmgren-Miner rule. Comput. Mater. Sci. 21, 101–110 (2001)

    Article  Google Scholar 

  6. Vasudevan, A.K., Sadananda, K., Iyyer, N.: Fatigue damage analysis: issues and challenges. Int. J. Fatigue 82, 120–133 (2016)

    Article  Google Scholar 

  7. Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics. Springer, Berlin (2005)

    Google Scholar 

  8. Elshelby, J.D.: The determination of the elastic field of an ellipsoidal inclusion and related problems. Proc. R. Soc. Lond. A241, 376–396 (1957)

    ADS  MathSciNet  Google Scholar 

  9. Hill, R.: Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101 (1965)

    Article  ADS  Google Scholar 

  10. Hill, R.: On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. Lond. A241, 131–147 (1972)

    ADS  MATH  Google Scholar 

  11. Iwakuma, T., Nemat-Nasser, S.: Finite elastic-plastic deformation of poly-crystalline metals. Proc. R. Soc. Lond. A394, 87–119 (1984)

    ADS  MATH  Google Scholar 

  12. Kröner, E.: On the plastic deformation of polycrystals. Acta Metallurgica 9, 155–161 (1961)

    Article  Google Scholar 

  13. Berveiller, M., Zaoui, A.: Self-consistent schemes for heterogeneous solid mechanics. In Comportement Rhéologique et Structure des Matériaux, CR 15è coll. GFR, Paris (1980)

  14. Pierard, O., Gonzalez, C., Segurado, J., et al.: Micromechanics of elasto-plastic materials reinforced with ellipsoidal inclusions. Int. J. Solids Struct. 44, 6945–6962 (2007)

    Article  Google Scholar 

  15. Lemaitre, J.: A Course on Damage Mechanics. Springer, Berlin (1992)

    Book  Google Scholar 

  16. Lemaitre, J., Desmorat, R., Sauzay, M.: Anisotropic damage law of evolution. J. Mech. Theor. Appl. 19, 187–208 (2000)

    MATH  Google Scholar 

  17. Lemaitre, J., Doghri, I.: Damage 90: a post processor for crack initiation. Comput. Method Appl. Mech. Eng. 115, 197–232 (1994)

    Article  ADS  Google Scholar 

  18. Lemaitre, J., Sermage, J.P., Desmorat, R.: A two scale damage concept applied to fatigue. Int. J. Fract. 97, 67–81 (1999)

    Article  Google Scholar 

  19. Laiarinandrasana, L., Morgeneyer, T.F., Cheng, Y., et al.: Microstructural observations supporting thermography measurements for short glass fibre thermoplastic composites under fatigue loading. Continuum Mech. Thermodyn. 32, 451–469 (2020). https://doi.org/10.1007/s00161-019-00748-4

    Article  ADS  Google Scholar 

  20. Sun, B., Xu, Y.L., Li, Z.: Multi-scale fatigue model and image-based simulation of collective short cracks evolution process. Comput. Mater. Sci. 117, 24–32 (2016)

    Article  Google Scholar 

  21. Lautrou, N., Thevenet, D., Cognard, J.Y.: Fatigue crack initiation life estimation in a steel welded joint by the use of a two-scale damage model. Fatigue Fract. Eng. Mater. Struct. 32(5), 403–417 (2009)

    Article  Google Scholar 

  22. Qian, C., Westphal, T., Nijssen, R.P.L.: Micro-mechanical fatigue modelling of unidirectional glass fibre reinforced polymer composites. Comput. Mater. Sci. 69(1), 62–72 (2013)

    Article  Google Scholar 

  23. Lemaitre, J., Sermage, J.P.: One damage law for different mechanisms. Comput. Mech. 20, 84–88 (1997)

    Article  Google Scholar 

  24. Eggertsen, P., Mattiasson, K.: On the identification of kinematic hardening material parameters for accurate springback predictions. Int. J. Mater Form 4, 103–120 (2011)

    Article  Google Scholar 

  25. Bathe, K.J., Montans, F.J.: On modeling mixed hardening in computational plasticity. Comput. Strut. 82(6), 535–539 (2004)

    Article  Google Scholar 

  26. Nijssen, R.P.L., Van Delft, D.R.V., Van Wingerde, A.M.: Alternative fatigue lifetime prediction formulations for variable-amplitude loading. J. Sol. Energy Eng. 124(4), 396–403 (2002)

    Article  Google Scholar 

  27. Burger, M., Wolfram, M.: Numerical approximation of an SQP-type method for parameter identification. SIAM J. Numer. Anal. 40, 1775–1797 (2002)

    Article  MathSciNet  Google Scholar 

  28. Miner, M.A.: Cumulative damage in fatigue. J. Appl. Mech. 14, A159–164 (1945)

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China (51375386).

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Correspondence to Q. Sun.

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Communicated by Andreas Öchsner.

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Liu, X.R., Sun, Q. An improved macro–micro-two-scale model to predict high-cycle fatigue life under variable amplitude loading. Continuum Mech. Thermodyn. 33, 803–816 (2021). https://doi.org/10.1007/s00161-020-00958-1

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  • DOI: https://doi.org/10.1007/s00161-020-00958-1

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